An identity involving 3-regular graphs
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Abstract It is proved that, if M is a perfect matching in a 3-regular graph G , then the number of positive-minus-negative M -covers of G is equal to the number of positive-minus-negative M -partitions of G . Moreover, either there are no M -partitions of G , or every M -partition and every M -cover has the same sign.
[1] Douglas R. Woodall,et al. Bond Graphs II: Causality and Singularity , 1997, Discret. Appl. Math..